Summary
New Green's functions are given, with properties such that the Coulomb scattering wave functions satisfy the corresponding integral equations. Solutions of these equations with various screened Coulomb potentials, therefore, obtain finite phase in the limit of vanishing screening. The treatment is extended to the time-dependent and to the relativistic cases.
Riassunto
Si danno nuove funzioni di Green con proprietà tali che le funzioni d'onda dello scattering di Coulomb soddisfino le corrispondenti equazioni integrali. Soluzioni di queste equazioni con vari potenziali di Coulomb schermati ottengono perciò una fase finita nel limite della schematura tendente a zero. Si estende il trattamento al caso dipendente dal tempo e al caso relativistico.
Резюме
Предлагаются новые функции грина, которые обладают такими свойствами, что волновые функции кулоновского рассеяния удовлетворяют соответствующим интегральным уравнениям. Решения этих уравнений с различными зкранированными кулоновскими приводят к конечной фазе в пределе, когда зкранировка исчезает. Предложенный подход обобщается на случай потенциала, зависящего от времени и на релятивистский случай.
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Kolsrud, M. Integral equations for Coulomb states. Nuovo Cim B 38, 61–74 (1977). https://doi.org/10.1007/BF02726211
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DOI: https://doi.org/10.1007/BF02726211